4 2 4 THE SCIENCE OF LOGIC 



Some men are either knaves or fools. Contradict (a) the proposition, &quot; No men 

 are both honest and prosperous in business&quot; ; express the original (b] as an 

 alternative proposition ; (c} as a conditional proposition. Contradict (b\ and 

 (c) ; and show that the three contradictories are equivalent. 



PART III. 



CHAP. I. Distinguish mediate from immediate inference. Explain 

 major and minor extremes, premisses, conclusion, middle term. Give some 

 definitions of mediate reasoning. Define the Syllogism. Distinguish be 

 tween the matter and ihzform of the syllogism ; the remote and the proxi 

 mate matter. Which is the major premiss of a syllogism ? Can you tell 

 this without knowing the conclusion ? How is the formal element of the 

 syllogism expressed ? Does the formal validity of a syllogism guarantee the 

 truth of its conclusion absolutely, or only conditionally ? Explain and justify 

 the axiom : &quot; Ex f also sequitur quodlibet &quot;. Why is it possible to reach a true 

 conclusion through false premisses ? Why can we not infer the truth of the 

 premisses from the truth of the conclusion, though we can infer the falsity of 

 (one at least of) the premisses from the falsity of the conclusion ? What 

 fallacies arise from not attending to those points ? Enumerate the various 

 kinds of syllogisms, and describe each. Does the syllogism presuppose the 

 fundamental laws of thought ? Is it an application of them ? And of them 

 alone ? What do you understand by a Mediate Axiom of the syllogism ? 

 State the mediate axioms of Identity and Diversity. Are they mathematical ? 

 What form of syllogism did Aristotle regard as the perfect or standard form ? 

 Explain : &quot; Syllogistic reasoning is from the general to the particular &quot;. State 

 and explain the Aristotelean Dictum. Investigate the question whether it 

 refers us to the extension, or the intension, or both, of P, S, and M respec 

 tively. How is M to be read in the major premiss ? Suggest a modified 

 reading of the Dictum which will show more clearly the inferential character 

 of the syllogistic process ? Indicate some mediate axioms based exclusively 

 on the intensive aspect of the terms of the syllogism. 



CHAP. II. Derive the general rules of syllogism from the Aristotelean 

 Dictum. Enunciate these rules. What practical use have the rules of 

 structure ? What is Quaternio Terminorum ? Undistributed Middle ? Ex 

 plain why the middle term must be distributed at least once. Illustrate by 

 Euler s circles. Explain Illicit Major and Illicit Minor. Illustrate each by 

 an example of your own. Why can illicit major not occur in affirmative 

 syllogisms? Prove the rule that one premiss must be affirmative. Illustrate 

 it by Euler s circles. Can a conclusion be ever validly inferred from two 

 negative propositions? If so, is the present rule thereby disproved? Give 

 some instances of similar apparent violations of the rules of quantity. Prove 

 that a negative premiss necessitates a negative conclusion, and vice versa; 

 that two particular premisses yield no conclusion ; that &quot; the conclusion 

 follows the weaker premiss &quot; ; that a particular major and a negative minor 

 yield no conclusion. Why must the premisses always distribute one term 

 more than the conclusion ? Show that either premiss of a valid syllogism, 

 combined with the denial of the conclusion, must prove the denial of the other 

 premiss. Show that illicit process in the former syllogism will involve undis- 



